Abstract
The theory of the conservation of energy in the thin layer approximation has been extended to special relativity. Four models for the density of the circumstellar medium are analyzed, which are represented by constant, power law, exponential and Emden (n = 5) profile for density. The astrophysical results are presented in a numerical way, except for a Taylor expansion of the four trajectories in the surrounding of the origin. The free parameters of the models are particularized for SN1993j, for which the radius versus time is known. Some evaluations on the time dilation are presented.
Highlights
The production of relativistic electrons in the early phase of a supernova (SN) is an active field of research
Previous studies analyzed the relativistic conservation of momentum for the thin layer approximation adopting a power law profile of the density, see [12], and a Lane Emden (n = 5) profile of density, see [13]
We recall that the relativistic conservation of the momentum or the energy in the thin layer approximation is a hypothesis of work that should be sustained from the observations, i.e. the observed trajectory of SN 1993J [14]
Summary
The production of relativistic electrons in the early phase of a supernova (SN) is an active field of research. The application of the non-relativistic perpendicular shocks to: 1) the formation of Weibel-type filamentation instabilities, which generate magnetic turbulence, see [1]; 2) the shock-surfing acceleration of electrons at the leading edge of the shock foot and downstream of the shock, see [2] [3]; and 3) studying the magnetic re-connection as a dominant acceleration process for the acceleration of the electrons, see [4].
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